Garcia (9-3) pitched seven strong innings, Ozuna had a career-high four hits and Widger went 3-for-4 as Chicago improved to 28-5 against AL Central teams, including 8-3 over Cleveland.
"You play so many games in the division, it is important to do well against those teams because that determines your season," Guillen said.
The Indians fell to 15-23 in the division, lost for the seventh time in eight games overall and fell 13 games behind first-place Chicago. They have scored one run in two games against the White Sox to start the second half.
Chicago scored four runs in the first inning off C.C. Sabathia
(6-6) and Garcia made it stand up. The right-hander allowed one run and six hits to improve to 6-0 in 11 starts since losing to Baltimore on May 14.
"With four runs in the first, I just tried to go out and pitch my game," Garcia said. "I got two double plays. It seems that no matter what this team needs, we get it done."
Garcia struck out four and walked three as he moved to 14-2 with a 2.69 ERA over his last 18 road starts since the start of the 2004 season.
Sabathia struck out a season-high nine over five innings but also gave up six hits, four runs and four walks. He pitched scoreless ball after a first inning in which he threw 44 pitches -- 23 after getting what should have been the third out.
"When you talk effort-wise, it's the best he's been this year," Indians manager Eric Wedge said of the left-hander. "Obviously, things weren't going his way, but he regrouped and
Sabathia issued two-out walks to Frank Thomas and Paul Konerko
in the first. Carl Everett then struck out on a wild pitch but reached first to load the bases as the ball got past catcher Victor Martinez.
"There's two outs and the ball's in the dirt, so you run," Everett said. "You never know what might happen and it did. This team takes advantage of opportunities like that."
Martinez blamed himself.
"I got lazy and didn't block the ball," he said. "It was a good pitch. We should have been out of the inning."
Jermaine Dye walked on a 3-2 pitch to force home one run. Aaron Rowand then lined a 3-2 pitch for a two-run single. Center fielder Grady Sizemore tried to make a diving catch but trapped the ball. Widger followed with an RBI single for a 4-0 lead before Sabathia finally struck out Juan Uribe for the fourth out.
"We've been a little lucky, but you make your own luck," Widger said. "Those guys in that inning had some good at-bats, fouling off pitches against a guy throwing 97, 98 mph."
Matt Miller replaced Sabathia to start the sixth and made only five pitches before leaving with a tight right forearm after allowing a single to Widger.
David Riske came on and gave up a one-out single to Ozuna that sent Widger to third. Ozuna then stole second; when Martinez threw wildly, Widger scored and Ozuna went to third. Tadahito Iguchi then put down a perfect suicide-squeeze bunt to score Ozuna and make it 6-1.
Ozuna, in his 36th game, raised his average from .286 to .312. Widger, in his 26th game, hiked his average 24 points to .280. He had an RBI single in the eighth.
The White Sox went 3-for-4 in steal attempts, making them 7-for-10 in two nights against Martinez. ... Sabathia fell to 8-3 with a 4.18 ERA in 14 career starts against the White Sox. ... Indians right fielder Casey Blake is in an 0-for-13 slump and Sizemore has hit .169 (10-for-59) over 13 games. ... Garcia is 5-0 with a 1.66 ERA in six starts against the AL Central. ... Ozuna is hitting .380 (19-for-50) on the road.